Nef line bundles on Calabi-Yau threefolds, I

TL;DR

This paper proves that certain nef line bundles on Calabi-Yau threefolds with specific conditions are semiample, advancing understanding of line bundle properties in algebraic geometry.

Contribution

It establishes semi-ampleness of nef line bundles with non-zero square Chern class on Calabi-Yau threefolds with Picard number 2 and non-zero third Chern class, under new conditions.

Findings

Nef line bundles with $c_1(\\mathcal L)^2 \ne 0$ are semiample on specified Calabi-Yau threefolds.

Semi-ampleness holds for line bundles with these properties when Picard number is 2.

The result applies to Calabi-Yau threefolds with non-zero third Chern class.

Abstract

We prove that a nef line bundle $\mathcal L$ with $c_1(\mathcal L)^2 \ne 0$ on a Calabi-Yau threefold $X$ with Picard number $2$ and with $c_3(X) \ne 0$ is semiample, that is, some multiple of $\mathcal L$ is generated by global sections.